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GeoGebra is an open source mathematics education software tool being used in thousands of schools worldwide. Since version 4.2 (December 2012) it supports symbolic computation of locus equations as a result of joint effort of mathematicians…

An increasingly common area of study in procedural content generation is the creation of level segments: short pieces that can be used to form larger levels. Previous work has used basic concatenation to form these larger levels. However,…

The problem of mating two parts with low clearance remains difficult for autonomous robots. We present bi-level belief assembly (BILBA), a model-based planner that computes a sequence of compliant motions which can leverage contact with the…

We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex…

Classical and exceptional Lie algebras and their representations are among the most important tools in the analysis of symmetry in physical systems. In this letter we show how the computation of tensor products and branching rules of…

Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of…

Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…

A summary of an experimental course on algebraic curves is given that was held for young learners at age 11. The course was a part of Epsilon camp, a program designed for very gifted students who have already demonstrated high interest in…

This paper presents the web-based platform Machine Learning with Bricks and an accompanying two-day course designed to teach machine learning concepts to students aged 12 to 17 through programming-free robotics activities. Machine Learning…

We study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse…

Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…

Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…

The paper describes an automated evaluation system for the learning of general Physics. The system whose name is Test on Line (ToL) is based on a questions bank from which an appropriate software generates individual multi-issue…

Entity linking (mapping ambiguous mentions in text to entities in a knowledge base) is a foundational step in tasks such as knowledge graph construction, question-answering, and information extraction. Our method, LELA, is a modular…

Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also computer scientists. Already in 1876, Kempe proposed a…

In programming education, it makes a difference whether you are dealing with beginners or advanced students. As our future students will become even more tech-savvy, it is necessary to assess programming skills appropriately and quickly to…

A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.

Large language models (LLMs) have the potential to revolutionize how we design and implement compilers and code translation tools. However, existing LLMs struggle to handle long and complex programs. We introduce LEGO-Compiler, a novel…

Manipulation and insertion of small and tight-toleranced objects in robotic assembly remain a critical challenge for vision-based robotics systems due to the required precision and cluttered environment. Conventional global or wrist-mounted…

Writing complex computer programs to study scientific problems requires careful planning and an in-depth knowledge of programming languages and tools. In this chapter the importance of using the right tool for the right problem is…